EXISTENCE RESULTS FOR STAMPACHIA AND MINTY TYPE VECTOR VARIATIONAL INEQUALITIES

In this paper, we consider more general forms of Stampacchia and Minty type vector variational inequalities for bifunctions and establish the existence of their solutions in the setting of topological vector spaces. We extend these vector vari- ational inequalities for set-valued maps and prove the existence of their solutionsin the setting of Banach spaces as well as topological vector spaces. We point out that our vector variational inequalities extend and generalize several vectorvariational inequalities appeared in the literature. As applications, we establish some existence results for a solution of vector optimization problem by usingStampacchia and Minty type vector variational inequalities.

کلیدواژه ها:

Stampacchia and Minty type vector variational inequalities ، Pseu- domonotonicity ، Cx-quasiconvex-like functions ، Vector optimization problem